If you are serious about studying "harmonic analysis" we recommend that:
(a) download a freeware copy of a good spectrum analysis software application from the Internet. This widely used research tool allow the user to analyze any acoustics waveform available at the computer's microphone input.
(b) Read the late John Backus' book “The Acoustical Foundations of Music” Second Edition, W.W. Norton and Company, New York, 1977. An outline of the book's introduction follows.
"Exploration of the relationship between science/mathematics and music has occupied many of the great minds of
history: Pythagoras, Aristotle, Ptolemy, Huyghens, Euler, Ohm, Young, Helmholtz, and many others.
• Since it is possible to examine music from a scientific perspective, it is valid to apply the process known as the
scientific method in the quantitative study of music and acoustics.
• Experimentation, and the subsequent interpretation of the results, can provide a set of laws and principles that can
explain physical behaviors. We must keep in mind, however, that any conclusions are open for skepticism and scrutiny,
for history has shown that the scientific truths of one generation may be refuted by the research of the next generation.
• “A more practical reason for the study of acoustics of music is to acquaint the musician with the basis of his craft, and
enable him to understand which physical things are important to it and which are not. He should know, for example,
that a rise in air temperature affects the intonation of the winds, and not of the strings.” (p. xiv)
• Simply put, the more you know about acoustics and the more you understand the physics of sound, the better
equipped you are to deal with any number of questions or situations that occur in the practice of musicmaking. The
practical value of this knowledge cannot be overstated, so long as the individual actively seeks to integrate the
information into action."
Both of the above recommendations will "co$t" you far less than the price of many electronic tuning devices.
If, as a result of your studies, you develop a new or unique tuning temperament, let us know. Rarely does the musician (JS Bach excepted) advance the science of sound. That task is usually left to the scientist, the researcher or the tinkerer.
Notes on Mr Backus' book is available at this link.http://emu.music.ufl.edu/downloads/backus-intro-thru-3.pdf